A class of hybrid algebraic multilevel preconditioning methods (Q1917430)

A class of hybrid algebraic multilevel preconditioning methods is presented for solving systems of linear equations with symmetric positive definite matrices resulting from the discretization of second-order elliptic boundary value problems by the finite element method. The new preconditioners are shown to be of optimal orders of complexity for two-dimensional and three-dimensional problem domains, and their relative condition numbers are estimated to be bounded uniformly with respect to the numbers of both levels and nodes.